an adaptive h-refinement algorithm for local damage models局部损伤模型的自适应h-refinement算法.pdfVIP

Algorithms 2009, 2, 1281-1300; doi:10.3390/a2041281 OPEN ACCESS algorithms ISSN 1999-4893 /journal/algorithms Article An Adaptive -Refinement Algorithm for Local Damage Models Jonathan S. Pitt and Francesco Costanzo Department of Engineering Science and Mechanics, The Pennsylvania State University, 212 EES Building, University Park, PA 16802, USA; E-mail: jsp203@ Author to whom correspondence should be addressed; E-mail: costanzo@. Received: 30 April 2009; in revised form: 18 September 2009 / Accepted: 28 September 2009 / Published: 6 October 2009 Abstract: An adaptive mesh refinement strategy is proposed for local damage models that often arise from internal state variable based continuum damage models. The proposed al- gorithm employs both the finite element method and the finite difference method to integrate the equations of motion of a linear elastic material with simple isotropic microcracking. The challenges of this problem include the time integration of coupled partial differential equa- tions with time-dependent coefficients, and the proper choice of solution spaces to yield a stable finite element formulation. Discontinuous elements are used for the representation of the damage field, as it is believed that this reduction in regularity is more consistent with the physical nature of evolving microcracking. The adaptive mesh refinement algorithm relies on custom refinement indicators, two of which are presented and compared. The two refine- ment indicators we explore are based on the time rate of change of the damage field and on the energy